How do you write an equation of a line that passes through the point (3, 2) and is parallel to the line y=3x-4?

Question

Ethan Adkins · Accepted Answer

#y - 2= 3(x - 3)# or #y = 3x - 7#

For a line to be parallel to another line, by definition it must have the same slope. Because the equation is in the slope-intercept form we can use the slope of the line.

The slope-intercept form of a linear equation is:

#color(red)(y = mx + b)# Where #m# is the slope and #b# is the y-intercept value.

Therefore, for the given equation the slope is #3#.

Now we can use the point slope formula to determine the equation for the parallel line.

The point-slope formula states: #color(red)((y - y_1) = m(x - x_1))# Where #m# is the slope and #(x_1, y_1) is a point the line passes through.

Substituting the slope from the given line and the given point gives:

#y - 2= 3(x - 3)#

Transforming this to the slope-intercept form by solving for #y# gives:

#y - 2 = 3x - 9#

#y - 2 + 2 = 3x - 9 + 2#

#y = 3x - 7#

Eva Adamson · Answer

undefined To write an equation of a line parallel to $ y = 3x - 4 $ and passing through the point $ (3, 2) $, you use the slope of the given line, which is $ 3 $, and then plug in the coordinates of the given point into the point-slope form of the equation $ y - y_1 = m(x - x_1) $. This yields $ y - 2 = 3(x - 3) $. Simplifying, you get $ y - 2 = 3x - 9 $, which simplifies further to $ y = 3x - 7 $. Therefore, the equation of the line is $ y = 3x - 7 $.